An Investigation Into the Impact of Band Error Variance Estimation on Intrinsic Dimension Estimation in Hyperspectral Images

Abstract

There have been a significant number of recent papers about hyperspectral imaging, which propose various methods for estimating the number of materials/endmembers in hyperspectral images. This is sometimes called the “intrinsic” dimension (ID) of the image. Estimation of the error variance in each spectral band is a critical first step in ID estimation. The estimated error variances can then be used to preprocess (e.g., whiten) the data, prior to ID estimation. A range of variance estimation methods have been advocated in the literature. We investigate the impact of five variance estimation methods (three using spatial information and two using spectral information) on five ID estimation methods, with the aid of four different, but semirealistic, sets of simulated hyperspectral images. Our findings are as follows: first, for all four sets, the two spectral variance estimation methods significantly outperform the three spatial methods; second, when used with the spectral variance estimation methods, two of the ID estimation methods (called random matrix theory and NWHFC) consistently outperform the other three ID estimation methods; third, the better spectral variance estimation method sometimes gives negative variance estimates; fourth, we introduce a simple correction that guarantees positivity; and fifth, we give a fast algorithm for its computation.